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1. A blueprint for truncation resonance placement in elastic diatomic lattices with unit cell asymmetry

   https://doi.org/10.1121/10.0027939  

   Al_Ba'ba'a, Hasan_B; Yousef, Hosam; Nouh, Mostafa (July 2024, JASA Express Letters)

   Elastic periodic lattices act as mechanical filters of incident vibrations. By and large, they forbid wave propagation within bandgaps and resonate outside them. However, they often encounter “truncation resonances” (TRs) inside bandgaps when certain conditions are met. In this study, we show that the extent of unit cell asymmetry, its mass and stiffness contrasts, and the boundary conditions all play a role in the TR location and wave profile. The work is experimentally supported via two examples that validate the methodology, and a set of design charts is provided as a blueprint for selective TR placement in diatomic lattices. 

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2. The Role of Frequency and Impedance Contrasts in Bandgap Closing and Formation Patterns of Axially-Vibrating Phononic Crystals

   https://doi.org/10.1115/1.4063815  

   Al Ba’ba’a, Hasan B.; Nouh, Mostafa (March 2024, Journal of Applied Mechanics)

   Bandgaps, or frequency ranges of forbidden wave propagation, are a hallmark of phononic crystals (PnCs). Unlike their lattice counterparts, PnCs taking the form of continuous structures exhibit an infinite number of bandgaps of varying location, bandwidth, and distribution along the frequency spectrum. While these bandgaps are commonly predicted from benchmark tools such as the Bloch-wave theory, the conditions that dictate the patterns associated with bandgap symmetry, attenuation, or even closing in multi-bandgap PnCs remain an enigma. In this work, we establish these patterns in one-dimensional rods undergoing longitudinal motion via a canonical transfer-matrix-based approach. In doing so, we connect the conditions governing bandgap formation and closing to their physical origins in the context of the Bragg condition (for infinite media) and natural resonances (for finite counterparts). The developed framework uniquely characterizes individual bandgaps within a larger dispersion spectrum regardless of their parity (i.e., odd versus even bandgaps) or location (low versus high-frequency), by exploiting dimensionless constants of the PnC unit cell which quantify the different contrasts between its constitutive layers. These developments are detailed for a bi-layered PnC and then generalized for a PnC of any number of layers by increasing the model complexity. We envision this mathematical development to be a future standard for the realization of hierarchically structured PnCs with prescribed and finely tailored bandgap profiles. 

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3. Understanding the role of resonances and anti-resonances in shaping surface-wave bandgaps for metasurfaces

   https://doi.org/10.1063/5.0093083  

   Pillarisetti, Lalith Sai; Lissenden, Cliff J.; Shokouhi, Parisa (October 2022, Journal of Applied Physics)

   An array of surface-mounted prismatic resonators in the path of Rayleigh wave propagation generates two distinct types of surface-wave bandgaps: longitudinal and flexural-resonance bandgaps, resulting from the hybridization of the Rayleigh wave with the longitudinal and flexural resonances of the resonators, respectively. Longitudinal-resonance bandgaps are broad with asymmetric transmission drops, whereas flexural-resonance bandgaps are narrow with nearly symmetric transmission drops. In this paper, we illuminate these observations by investigating the resonances and anti-resonances of the resonator. With an understanding of how the Rayleigh wave interacts with different boundary conditions, we investigate the clamping conditions imposed by prismatic resonators due to the resonator’s resonances and anti-resonances and interpret the resulting transmission spectra. We demonstrate that, in the case of a single resonator, only the resonator’s longitudinal and flexural resonances are responsible for suppressing Rayleigh waves. In contrast, for a resonator array, both the resonances and the anti-resonances of the resonators contribute to the formation of the longitudinal-resonance bandgaps, unlike the flexural-resonance bandgaps where only the flexural resonances play a role. We also provide an explanation for the observed asymmetry in the transmission drop within the longitudinal-resonance bandgaps by assessing the clamping conditions imposed by the resonators. Finally, we evaluate the transmission characteristics of resonator arrays at the anti-resonance frequencies by varying a few key geometric parameters of the unit cell. These findings provide the conceptual understanding required to design optimized resonators based on matching anti-resonance frequencies with the incident Rayleigh wave frequency in order to achieve enhanced Rayleigh wave suppression. 

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4. Analysis of geometric defects in square locally resonant phononic crystals: A comparative study of modeling approaches

   https://doi.org/10.1121/10.0022330  

   Katch, L.; Moghaddaszadeh, M.; Willey, C. L.; Juhl, A. T.; Nouh, M.; Argüelles, A. P. (November 2023, The Journal of the Acoustical Society of America)

   Vladislav Sergeevich Sorokin (Ed.)

   Phononic crystals can develop defects during manufacturing that alter the desired dynamic response and bandgap behavior. This frequency behavior change can enable successful defect inspection if the characteristic defect response is known. In this study, the behavior of a defective square unit cell comprising a freed and shortened leg is studied using a wave finite element method and an approximate continuous-lumped model to elucidate the defect induced qualitative dynamical features. These metrics are a computationally inexpensive alternative to modeling a defective unit cell within a large pristine array entirely in finite elements. The accuracy of these models is validated by comparing the result to a full finite element model. The impact of a shortened unit cell leg on the behaviors of an infinite array of defective cells and a finite array with a single defect are successfully predicted through dispersion curves and frequency response functions, respectively. These methods reveal defect-induced modes that split the local resonance bandgap of the pristine cell, as well as new anti-resonances resulting from the shortened leg. The study uses both approaches to evaluate the effect of defects in complex phononic crystal geometries and provides a comparative evaluation of the results of each model. 

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5. Resonance excitation of atmospheric waves by vibration of the ground, ocean surface, and ice shelves

   https://doi.org/EGU2018/EGU2018-5584  

   Goin, O. A.; Zabotin, N. (January 2018, Geophysical research abstracts)

   null (Ed.)

   Atmosphere is known to respond in a resonant way to broad-band excitation associated with earthquakes, volcano eruptions, and convective storms. The resonances are observed via their ionospheric manifestations using HF Doppler radars, airglow observations, and the GPS-TEC technique and are seen as narrow frequency bands of greatly amplified oscillations. The resonances are normal modes of an atmospheric waveguide and occur at such frequencies that an acoustic-gravity wave, which is radiated at the ground level and is reflected from a turning point in the thermosphere or upper mesosphere, upon return to the ground level satisfies boundary conditions on the ground. Typically, the resonances correspond to near-vertical AGW propagation and have periods of about 3–5 minutes. Although the resonances are usually referred to as acoustic resonances, buoyancy effects are not negligible at such frequencies. The resonances correspond to most efficient coupling between atmosphere and its lower boundary and are promising for detection of such coupling. From the remote sensing prospective, the resonances are potentially significant because their frequencies are sensitive to variations in the vertical profile of neutral temperature up to thermospheric altitudes and to boundary conditions on the lower boundary, such as differences between the boundary conditions on the solid earth, ocean surface, and a finite ice layer overlying solid Earth or the ocean. Using recently developed consistent WKB approximation for acoustic-gravity waves, this paper investigates theoretically excitation of atmospheric resonances and quantifies the effects of buoyancy and non-vertical propagation, including the contribution of the Berry phase. Different kinds of atmospheric resonances are identified depending on the type of surface waves, including flexural waves in ice shelves, that are responsible for oscillations at the ground or sea level. 

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